If you have an active subscription, don't have any enforcement action affecting your connection to the game servers and your privacy settings all enable/allow online multiplayer, then be sure that you're signed in to the correct account/profile.
Be sure your PC meets the minimum system requirements for Call of Duty: Modern Warfare II. If you're experiencing graphical issues in Call of Duty: Modern Warfare II, be sure to install the applicable video card drivers listed below. Nvidia: The recommended driver version for Call of Duty: Modern Warfare II is 526.86.
On the Microsoft Mahjong page in Microsoft Store, select Get the game (online) or Install (in Microsoft Store app). The game will download and install automatically. To launch the game, select Play.